The Boston Marathon bombings have ignited a debate in Washington and among terrorism analysts over how the wider threat facing the U.S. has evolved since the 9/11 attacks of 2001.

The Tsarnaev brothers, who spent a solid portion of their formative years as immigrants to one of America’s oldest cities, present a completely different dilemma than the 19 globe-trotting al Qaeda operatives who flew hijacked airplanes into the World Trade Center and the Pentagon nearly 12 years ago.

From an operational standpoint, the Boston case suggests that the core threat facing the U.S. has shifted from one of internationally financed and plotted mass carnage to something more akin to “lone-wolf type attacks that are less deadly but more difficult to disrupt,” said Joseph Young, a professor at American University who specializes in the causes and consequences of terrorism.

Seth Jones, associate director of the International Security and Defense Policy Center at the Rand Corp., said it highlights the growing radicalization problem America has to address.

“We’re seeing a rise in the number of individuals that are radicalizing in the United States and are plotting attacks without being members of an actual terrorist group,” Mr. Jones said. “If you look at a lot of the FBI arrests over the past several years, they’re individuals with nominal or no links with a terrorist organization overseas, but have simply been inspired to conduct attacks.”

He added that the “online component” in such cases is “increasingly important” because it opens a virtual world for anyone with an Internet connection to read jihadist websites and listen to online sermons by such extremist fomenters as Anwar al-Awlaki, a dual American-Yemini citizen who was killed by a U.S. drone strike in Yemen in 2011.

The fact that Tamerlan Tsarnaev, 26, and his 19-year-old brother, Dzhokhar, effectively grew up in the U.S. is important, said Mr. Young, who described their suspected terrorist action as a “mash-up between Faisal Shahzad, who tried to blow up Times Square in 2010 and the Columbine shooters in Colorado in 1999.”

“I think their motivation probably lies at the intersection of those two events,” he said. “Some sort of personal alienation mixed with a larger radical goal, which is poorly defined.”

A key part of the trend also appears to involve individuals, such as al-Awlaki, who straddle two worlds in their terrorist pursuits, keeping one foot in the U.S. while remaining — or becoming at some point in their young adulthood — emotionally connected to ideologies alive elsewhere on the planet.

One example is the 2009 case of Najibullah Zazi, an Afghan-American who pleaded guilty with two other defendants to plotting suicide bomb attacks on the New York City subway. In another case, Shahzad, a Pakistani-American citizen, confessed to attempting to carry out a car bombing in Times Square in 2010.

In both cases, the men “did go overseas for some training and then came back,” said Mr. Jones. “But they were Americans.”

The lack of a clear motive has prompted reflection among some on Capitol Hill, particularly among lawmakers briefed last week by the FBI on the probe into the Tsarnaevs’ activities before the Boston bombings — including a trip one of the brothers made to Chechnya last year.

The trip seems to suggest a connection to the Islamic extremists active in the break away Russian province, but the extent and relevance of such a connection has eluded authorities.

Alternatively, lawmakers said they were told during last week’s briefings that the Tsarnaev brothers likely learned bomb-making from jihadist websites — not from a terrorist school in a far-flung Muslim corner of the former Soviet Union.

“Probably the most profound questions that’s been raised by this is: Has the nature of the threat changed?” Rep. Adam B. Schiff said during a brief meeting with reporters after one of the FBI briefings Wednesday.

The California Democrat pondered aloud whether the narrative forming around the Tsarnaevs suggests America is “now facing more what Europe has faced” in recent years, with “an alienation of part of the immigrant population” leading to “self-radicalization.”

That would be a marked shift from the 9/11 era threat of terrorists who “trained overseas or receive material support from overseas and come here to attack us, and I think that will cause us to do some things differently,” Mr. Schiff said.

Other lawmakers warn that international terrorist organizations are increasingly looking to connect with potential operatives living in America.

“I hate to say it, but there are more of these people coming after us, and the new way of hitting America is to do it inside, and there’s efforts afoot by international terrorists to recruit American citizens for their cause and we can’t be right every time,” Sen. Lindsey Graham, South Carolina Republican, has told reporters on Capitol Hill.